Is there a shortcut key to horizontally flip a brush?

Another approach — albeit with limited functionality — is to create a new preset with the brush flipped, and use the existing shortcuts for Previous and Next preset.  Those being , (comma) and . (full stop). 

I did try to record an Action which did not work, and you'd need to record separate actions for flip on, and flip off even if it had.  So the script has to be cleanest solution.

Juliane Kost put up some useful information when the brush engine changed in 2017.  Her Blog Page  

There was a Sneak Peek from MAX 2017, but I am not finding it!  😞 

Does the Script make the intended change? 

Did you do a Forum Search? 

Because @jazz-y »recently« posted a Script for the task and Scripts can be assigned shortcuts. 

Hi!

Not that I know of, the only way would be using the brushes settings panel

all the shortcuts (that can be modified BTW) can be found in the keyboard shortcuts section (in the edit menu)

you can use the drop down menu to switch from tool to menus at the top.
The only thing that you could do is to duplicate your chosen brush, flip it using the brushes settings, so you got two brushes : normal and flipped, and use the "previous brush", "next brush" to which is keyboard shortcut is available.

Now I am assuming that you want to flip a brush, not the result of the painting on a layer...